Last Sunday Andy Murray did something he's never done before. No, not the part about him beating Roger Federer at a Wimbledon final. Murray sang the British national anthem on the podium as he picked up his Olympic gold.

Fortunately only the first verse of God Save The Queen gets sung at Olympics medal ceremonies - no mention of those "Rebellious Scots to crush" buried away later in the lyrics. Even so, it put Murray in a fairly onerous position - don't sing along and he's unpatriotic and dour, mouth along the words and people call him a traitor. The poor guy couldn't win either way.

Andy Murray could be holding up a Scottish flag come the Rio Olympics in 2016

Let's leave aside the fact the Queen would still be reigning over Murray and all other Scots in the event of independence, though. The more interesting debate is about how over the past week unionist politicians and commentators, Labour and Tory alike, have claimed that the astonishing performance of Team GB says something about the importance of keeping the UK together.

Gordon Brown became the latest voice in a clamour of pro-union bluster on Monday, when he told an audience in Edinburgh: "When we pull and share resources for the common good, it's often the case that the benefit is far greater than would have occurred if we had just summed up and added up the parts."

He added: "The Olympics is pretty clear to us that by the pooling of resources in, say, cycling we managed to do what if you just divided the money and put a tenth to Scotland and a tenth to Yorkshire and so on you could not have achieved the same results."

In two year’s time precisely the opposite arguments will be made when Glasgow hosts the Commonwealth Games. As always, Scotland will be fielding its own separate team and if the performance of Scottish athletes at London 2012 is anything to go by, they can expect to improve on their performance in the Delhi games of 2010. The SNP is at pains to point out that Scottish athletes were responsible for nearly a third of Team GB's medals haul over the past fortnight.

Some say that politicians shouldn't use sport to score political points. But it's hard for them not to, when the evidence shows sporting events can and do affect how people think about politics, including Scottish independence. Since the late 1970s, support for independence has hovered around the 30-35% mark, but in 1998 there was a brief and sudden surge, as this graph produced by IPSOS Mori Scotland clearly shows.

Is it a co-incidence that this was the last time Scotland was in the World Cup, almost holding their own against then world champions, Brazil? Or is it because it was the year of the successful devolution referendum? Of course, it's likely to be a bit of both, but what's interesting is that by the time the Scottish Parliament opened in 1999, support for independence was back down to its long-term average. It suggests something other than pure politics accounted for the surge.

Although a minor poll has been published in the wake of the Olympics, the next set of respected, series polls on Scottish independence will be published next month, and they'll be watched closely. The last two polls have shown a fairly big drop in support for separation. Talk of Alex Salmond botching the launch of the No campaign in May is almost certainly overblown, pollsters mostly attribute the drop to the Diamond Jubilee and the Olympics.

For a long time cynics have accused the SNP of wanting to hold the independence referendum straight after the Glasgow Commonwealth Games to capitalise on a similar surge. Privately the SNP are rubbing their hands with glee that Sir Chris Hoy will no longer have to train in Manchester because Scotland will have its own world-class velodrome.

Pointing out that Team GB's success is down to shared facilities ignores the fact that Scotland is about to get spanking new ones - and that in two year's time they'll make even the marvel of the Queen Elizabeth Olympic Park in Stratford look just slightly out of date.

Even if Team Scotland somehow does worse than expected in the 2014 Commonwealth Games, its prospects for holding a successful major sporting event seem assured, not least because it'll have learned the immediate lessons of London 2012. The fact the Ryder Cup returns to Gleneagles in the same year seems likely to further swell the sense of patriotism.

The Sir Chris Hoy Velodrome, under construction in Glasgow

For the time being the SNP are understandably dismissing any link between Team GB and Scotland's political future as rubbish. Scotland's culture spokesman at Westminster, Pete Wishart, tells me: "People are thoroughly tired and annoyed with unionist politicians trying to politicise this event. It's starting to really appall the Scottish people and we'll start to see a reaction to it."

Let's see in two year's time whether the SNP make similar noises, once the running shoe is on the other foot, when people like Andy Murray will be singing "Flower of Scotland" at the Glasgow games, a song that in all likelihood will become the country's permanent national anthem under independence.

Pro-union politicians like Brown may come to rue the day they tried to turn Team GB into a political pawn, because it won't be long before nationalists have just as much ammo to fire back. The risk for unionists is that a challenge is set, one that any sporting Scot would dearly love to rise to. And if there's one thing that's been proven over the past fortnight, it's the intangible power of home advantage.